1. Field of the Invention
The present invention aims to provide a novel articulated robot with the object of eliminating or reducing mechanical interference between arms or between arms and tools in the articulated robot.
2. Description of the Prior Art
Articulated robots are constructed from a plurality of arms, in which operation control is performed while interference extends between arms or between arms and tools.
FIGS. 8 and 17 show a model of a conventional horizontal articulated robot structure. Robot a is formed from a base shaft portion b, a first arm c and a second arm d, one end portion of the first arm c being attached to the base shaft b in a rotatable state. Also, one end of the second arm d is attached to the other end portion of the first arm c in a rotatable state, a tool mounting shaft e being provided at the other end of the second arm d.
A motor f and a harmonic reduction gear g are provided for rotating the first arm c on the base shaft portion b, the driving power of the motor f being transmitted as the rotating power of the first arm c via the harmonic reduction gear g.
A mechanism for rotating the second arm d is provided in the first arm c. For example, as shown in the drawing, a motor i and harmonic reduction gear j are attached to a support portion h fixed to the first arm c, and s pulley k is attached to an output shaft of the harmonic reduction gear j, l is a pulley forming a pair with the pulley k, and is fixed to the rotation shaft of the second arm d. Also, a belt m is extended between the pulley k and the pulley l. The driving power of the motor i becomes the rotating power for the pulley k via the harmonic reduction gear j, and this is transmitted to the pulley l by the belt m to become the rotating power of the second arm d.
FIG. 18 graphically expresses the structure when the robot a is viewed horizontally, the two-dimensional positional coordinates (X and Y) with a point of origin 0 as the rotational center of the first arm c being set to the base shaft portion b.
In FIG. 18 the point C indicates the rotational center of the second arm d, point E indicates a terminal position, the first arm c is indicated by the line OC (length "L1"), and the line CE (length "L2") indicates the second arm d. Also, the angle ".theta.1" indicates an angle formed by the line OC with respect to the X axis, and the angle ".theta.2" indicates an angle formed by the line CE with respect to an elongated line of line OC.
The point P1 and the point P2 respectively indicate the position of the center of gravity of the first arm c and the position of the center of gravity of the second arm d, the length of the line OP1 is made "l1" and the length of the line CP2 is made "12".
In leading through an equation of motion with respect to a power system model simplified in this manner, position, speed etc. can be expressed by means of a complex indicator by using a complex planar coordinate system taking the X axis as a real axis and the Y axis as an imaginary axis.
For example, the position of the center of gravity of each arm and the time differential of a first stage thereof are expanded to a complex amount and expresses as in the following equation. ##EQU1##
Note that here "i" is an imaginary unit.
Since the angle of rotation of the motor f is R1..theta.1 when the angle of rotation of the first arm c is .theta.1 and the angle of rotation of the motor i is R2..theta.2 when the angle of rotation of the second arm is .theta.2, where the total movement energy of the robot system is "Ek", we have the following equation. ##EQU2##
Since the square value of speed is obtained as the absolute value of a complex number, Ek is as follows. ##EQU3##
Since the potential energy is 0, upon applying [Equation 3] to the equation of motion ([Equation 4]) of each arm according to a Euler-Lagrange equation while taking care that the Langrangian is equal to Ek, the output torque of the harmonic reduction gear can be obtained as in [Equation 5]. ##EQU4##
Note that in the above equations the effect of the viscosity term of friction etc. is ignored. In [Equation 5], the first term on the right side of the first equation of T1 shows an inertia term and the second term the inertia force (torque) received from the second arm d, and also, the third term shows Coriolis force (torque) and the fourth term shows torque where centrifugal force extends to the first arm c due to the rotation of the second arm d.
Also, the first term on the right side of the second equation of T2 shows an inertia term and the second term the inertia force (torque) received from the first arm c, and also, the third term shows torque where centrifugal force extends to the second arm d due to the rotation of the first arm c.
With respect to the movement of each arm an interference term as well as an inertia term exists in the arms themselves, but since the absolute value of this interference term is substantially the same amount as the inertia term, it can be ignored.